S Sonja Georgievska

Retaining the probabilities in probabilistic testing theory

This paper considers the probabilistic may/must testing theory for processes having external, internal, and probabilistic choices. We observe that the underlying testing equivalence is too strong and distinguishes between processes that are observationally equivalent. The problem arises from the observation that the classical compose-and-schedule approach yields unrealistic overestimation of the probabilities, a phenomenon that has been recently well studied from the point of view of compositionality (de Alfaro/Henzinger/Jhala 2001, Cheung/Lynch/Segala/Vaandrager 2006), in the context of randomized protocols (Chatzikokolakis/Palamidessi 2007), and in probabilistic model checking (Giro/D’Argenio/Ferrer Fioriti 2009). To that end, we propose a new testing theory, aiming at preserving the probability information in a parallel context. The resulting testing equivalence is insensitive to the exact moment the internal and the probabilistic choices occur. We also give an alternative characterization of the testing preorder as a probabilistic ready-trace preorder.

Branching Bisimulation Congruence for Probabilistic Systems

The notion of branching bisimulation for the alternating model of probabilistic systems is not a congruence with respect to parallel composition. In this paper we first define another branching bisimulation in the more general model allowing consecutive probabilistic transitions, and we prove that it is compatible with parallel composition. We then show that our bisimulation is actually the coarsest congruence relation included in the existing branching bisimulation when restricted to the alternating model.

Probabilistic may/must testing: retaining probabilities by restricted schedulers

This paper considers the probabilistic may/must testing theory for processes having external, internal, and probabilistic choices. We observe that the underlying testing equivalence is too strong and distinguishes between processes that are observationally equivalent. The problem arises from the observation that the classical compose-and-schedule approach yields unrealistic overestimation of the probabilities, a phenomenon that has been recently well studied from the point of view of compositionality, in the context of randomized protocols and in probabilistic model checking. To that end, we propose a new testing theory, aiming at preserving the probability information in a parallel context. The resulting testing equivalence is insensitive to the exact moment the internal and the probabilistic choices occur. We also give an alternative characterization of the testing preorder as a probabilistic ready-trace preorder.

Composing systems while preserving probabilities

Restricting the power of the schedulers that resolve the nondeterminism in probabilistic concurrent systems has recently drawn the attention of the research community. The goal is to preserve the probabilistic behaviour of systems when composed, and at the same time, to guarantee compositionality for trace-like equivalences. In our previous work, we have defined a model of probabilistic systems with labels on the internal transitions, that restrict the power of the schedulers. A tracestyle equivalence for the same model, compatible with a synchronous parallel composition, was proposed. In the present paper we generalize the parallel composition to allow for action interleaving and synchronization on a given set of actions, combined with hiding afterwards. We propose a method for automatic labeling of the internal transitions that arise due to the parallel composition. These labels reflect the information that the components use in order to resolve the nondeterminism in the composition, and thus restrict the power of the schedulers. We show that our equivalence is compositional w.r.t. the parallel composition. We also define operational semantics that, besides the parallel composition, includes deadlock, and four types of choices - action, external, internal, and probabilistic.

Branching bisimulation congruence for probabilistic systems

A notion of branching bisimilarity for the alternating model of probabilistic systems, compatible with parallel composition, is defined. For a congruence result, an internal transition immediately followed by a non-trivial probability distribution is not considered inert. A weaker definition of branching bisimilarity for the same model has been given earlier. Here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version. To support the use of the present equivalence as a reduction technique, we also show that probabilistic CTL formulae are preserved by our equivalence, and we provide a polynomial-time algorithm deciding branching bisimilarity.

Performance analysis of χ models using discrete-time probabilistic reward graphs

We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and quantitative analysis of timed systems based on the modeling language chi. The extension proposed in this paper is based on timed branching bisimulation reduction followed by a tailored inclusion of probabilities and rewards. The approach is applied in an industrial case study of a turntable drill. The resulting performance measures are shown to be comparable to those obtained by existent methods of the chi environment, viz. simulation and continuous-time Markovian analysis.

Testing reactive probabilistic processes

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows that the equivalence is insensitive to the exact moment in time in which an internal probabilistic choice occurs, which is inherent from the original testing equivalence of De Nicola and Hennessy. We also show decidability of the testing equivalence for finite systems for which the complete model may not be known.

Probabilistic CSP: preserving the laws via restricted schedulers

Extending Communicating Sequential Processes (CSP) by preserving the distributivity laws for internal choice, in the presence of probabilistic choice, has been an open problem so far. The problem stems from a well known disagreement between probabilistic choice and nondeterministic choice, that raises congruence issues for parallel composition. Recently, it has been argued that the congruence issue can be resolved only by restricting the power of the schedulers that resolve the nondeterminism. In our previous work, we have restricted the schedulers by suitably labeling the nondeterministic transitions. We have defined a ready-trace equivalence and a parallel composition with hiding for which the equivalence is a congruence. In this paper, we generalize our model and give a CSP-style axiomatic characterization of the ready-trace equivalence. From the axiomatization it follows that all distributivity axioms for internal choice from CSP are preserved, and no new axioms are added.

On Compositionality, Efficiency, and Applicability of Abstraction in Probabilistic Systems

A branching bisimulation for probabilistic systems that is preserved under parallel composition has been defined recently for the alternating model. We show that besides being compositional, it is decidable in polynomial time and it preserves the properties expressible in probabilistic Computation Tree Logic (pCTL). In the ground-complete axiomatization, only a single axiom is added to the axioms for strong bisimulation. We show that the Concurrent Alternating Bit protocol can be verified using the process algebra and a set of recursive rules.